## PRP Records

### Probable Primes Top 10000

#### (293510 PRPs in the top)

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 9753 (2^311580+7)/591329 93790 Lelio R Paula 06/2013 9751 10^93790-123456789 93790 Robert Price 02/2020 9752 10^93790-157517 93790 Patrick De Geest 04/2020 9754 (49*10^93782+293)/9 93783 Robert Price 03/2021 9755 12^86900-77 93781 Lelio R Paula 06/2016 9756 2^311508-109769 93774 Enzo Doria 04/2014 9757 2^311486-1859621 93767 Enzo Doria 03/2016 9758 Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831 93765 Kurt Beschorner 04/2015 9759 (10^93811-1)/(9*968129521*2109997013*3280113810431*639637782545831) 93765 Gord Palameta 10/2018 9760 2^311471+311469 93763 Renaud Lifchitz 01/2003 9761 (88*10^93760-1)/3 93762 Robert Price 10/2017 9762 2^311426+79459 93749 Enzo Doria 06/2016 9763 21537^21634+21634^21537 93745 Norbert Schneider 04/2020 9764 2^311409+111546435 93744 Paul Bourdelais 10/2021 9765 (2^311360+3078)/2 93729 Stefano Morozzi 09/2020 9766 (2^311341+2186)/2 93723 Stefano Morozzi 09/2020 9767 (2^311313+774)/2 93715 Stefano Morozzi 09/2020 9769 2^311294+5775 93709 Lelio R Paula 03/2016 9768 25155^5312+5312^25155 93709 Hans Havermann 09/2020 9770 2^311252-1017 93697 Lelio R Paula 03/2016 9771 2^311247-112041 93695 Enzo Doria 06/2014 9772 7*10^93692-83 93693 Robert Price 09/2017 9773 2^311205-109645 93683 Enzo Doria 04/2014 9774 5^134027-84 93681 Lelio R Paula 04/2016 9775 (2^311148-1017)/557 93663 Lelio R Paula 06/2013 9776 (2^311027-2^155514+1)/5 93628 11/2006 9777 26748^3161+3161^26748 93614 Hans Havermann 08/2020 9778 3^196192-28 93608 Robert Price 12/2013 9779 216091#+261433 93606 Makoto Morimoto 12/2015 9780 5^133917+68 93604 Lelio R Paula 04/2016 9781 2^310924-1709 93598 Yves Minet 03/2013 9782 24555^6476+6476^24555 93587 Hans Havermann 08/2020 9783 (2^310867+734)/2 93580 Stefano Morozzi 09/2020 9784 (266*10^93577-11)/3 93579 Robert Price 09/2016 9785 (16*10^93577+161)/3 93578 Robert Price 05/2016 9786 3^196113-56 93570 Lelio R Paula 04/2016 9787 2^310806-110345 93562 Enzo Doria 05/2014 9788 3^196093+86 93561 Lelio R Paula 04/2016 9789 2^310780-2327 93555 Yves Minet 10/2013 9790 30^63332+41 93550 Lelio R Paula 08/2012 9791 (21181*2^310707+1)/21 93536 Lelio R Paula 06/2014 9792 8*5^133807+7 93528 Lelio R Paula 10/2014 9793 2^310686+8193 93526 Lelio R Paula 03/2016 9794 22681^13282+13282^22681 93520 Hans Havermann 09/2020 9795 2^310646+63 93514 Lelio R Paula 11/2012 9796 (77*10^93508+31)/9 93509 Robert Price 10/2015 9797 ((2^103536+1)^3-2)/3 93502 Serge Batalov 03/2023 9798 (1000907^15583+1)/1000908 93499 Faysal YAtim 04/2009 9799 (2*10^93497+7)/9 93497 Erik Branger 03/2011 9800 3^195958-112852 93496 Enzo Doria 07/2014 9801 2^310583+16385 93495 Lelio R Paula 03/2016 9802 (9913*2^310557-1)/35 93490 Lelio R Paula 04/2015 9803 9*7^110614+2 93481 Lelio R Paula 11/2014 9804 5*3^195914-2^195914 93476 Jon Grantham 08/2023 9805 (19*10^93467+83)/3 93468 Robert Price 08/2020 9806 2^310469-8295 93461 Lelio R Paula 03/2016 9807 2^310459-1159 93458 Yves Minet 11/2012 9808 6^120075-95 93437 Lelio R Paula 05/2016 9809 (2^310362+1758)/2 93428 Stefano Morozzi 09/2020 9810 256*19^73047+9 93412 Eric Chen 12/2022 9811 148^43041-147 93411 Norbert Schneider 05/2019 9813 2^310289+98327 93407 Yves Minet 11/2010 9812 fibonacci(446949)+3 93407 Jon Grantham 08/2023 9814 21769^19510+19510^21769 93395 Hans Havermann 08/2020 9815 2^310217-113143 93385 Enzo Doria 07/2014 9816 7^110494-68 93379 Lelio R Paula 04/2016 9817 2^310184-113093 93375 Enzo Doria 07/2014 9818 2^310180-110417 93374 Enzo Doria 05/2014 9819 gcd(V(1124905),5*F(224981)*(F(224981)-1)+1) 93372 Serge Batalov 04/2015 9820 (2^310173+3150)/2 93372 Stefano Morozzi 09/2020 9821 3^195669+68 93358 Lelio R Paula 04/2016 9822 10^93356+91 93357 Robert Price 04/2011 9823 10^93356-28313 93356 Patrick De Geest 08/2013 9824 (85*10^93346+23)/9 93347 Robert Price 11/2015 9825 (3^195648-5)/3158276 93342 Lelio R Paula 04/2013 9826 10^93333+191061 93334 Patrick De Geest 09/2022 9828 10^93333-4000001 93333 Robert Price 07/2021 9827 10^93333-44807 93333 Patrick De Geest 09/2022 9829 2^310006+213499 93322 Enzo Doria 09/2023 9830 3^195556+8680 93304 Lelio R Paula 04/2016 9831 2^309942-109991 93302 Enzo Doria 04/2014 9832 2^309926-1867301 93298 Enzo Doria 03/2016 9833 2^309924+85951 93297 Yves Minet 03/2011 9834 2^309896-4229 93288 Yves Minet 08/2018 9835 (86*10^93263-77)/9 93264 Robert Price 05/2016 9836 6^119836-125 93251 Lelio R Paula 05/2016 9837 (77*10^93249-257)/9 93250 Robert Price 10/2017 9838 21822^18749+18749^21822 93245 Hans Havermann 09/2020 9839 3^195430-2 93244 Theodore Burton 02/2007 9840 (13*10^93236+47)/3 93237 Robert Price 01/2017 9841 (67*10^93226-7)/3 93228 Robert Price 10/2017 9842 (86*10^93217-221)/9 93218 Robert Price 06/2017 9843 2^309637-16329 93211 Enzo Doria 04/2013 9844 (41*10^93207+49)/9 93208 Robert Price 04/2016 9845 2^309598+21529 93199 Enzo Doria 08/2023 9846 14^81312-57 93194 Lelio R Paula 06/2016 9847 41^57783-40 93192 Theodore Burton 02/2007 9848 3*10^93179-97 93180 Robert Price 08/2017 9849 5*7^110252-4 93175 Lelio R Paula 11/2014 9850 22022^16959+16959^22022 93140 Hans Havermann 08/2020 9851 83061!4-512 93137 Robert Price 11/2019 9852 25169^5016+5016^25169 93135 Hans Havermann 08/2020 9853 (483641^16384+1)/2 93135 Richard Fischer 02/2021 9854 2^309380-27 93133 Lelio R Paula 11/2012 9855 25653^4268+4268^25653 93127 Hans Havermann 08/2020 9856 (2^309355+1826)/2 93125 Stefano Morozzi 02/2021 9857 (2^309334+2710)/2 93119 Stefano Morozzi 09/2020 9858 23*10^93116-7 93118 Robert Price 03/2016 9859 (2^309270+3214)/2 93100 Stefano Morozzi 09/2020 9860 (29*10^93082+1)/3 93083 Robert Price 11/2015 9861 (2^309198+3738)/2 93078 Stefano Morozzi 09/2020 9862 (58*10^93062-13)/9 93063 Robert Price 09/2015 9863 (2^309138+1794)/2 93060 Stefano Morozzi 01/2021 9864 2^309131+1869383 93058 Enzo Doria 05/2016 9865 (2^309114+3610)/2 93053 Stefano Morozzi 09/2020 9866 2^309066-93 93039 Lelio R Paula 11/2012 9867 2^309063-113269 93038 Enzo Doria 07/2014 9868 3^194965+16 93022 Robert Price 10/2013 9869 (89*10^93019-737)/9 93020 Robert Price 01/2022 9870 2^308979+1869143 93012 Enzo Doria 05/2016 9871 5^133064+54 93008 Lelio R Paula 04/2016 9872 (2^308947+2750)/2 93003 Stefano Morozzi 01/2021 9873 (2^308905-509203)/119 92988 Lelio R Paula 06/2013 9874 (94*10^92981-49)/99 92981 Ray Chandler 07/2011 9875 (2*10^92976-17)/3 92976 Robert Price 08/2014 9876 24783^5642+5642^24783 92972 Hans Havermann 08/2020 9877 (472489^16384+1)/2 92969 Richard Fischer 01/2021 9878 2^308809+37967 92961 Phil Moore 03/2008 9879 (3^194825+5)/11656 92952 Lelio R Paula 04/2013 9880 14774^22291-22291^14774 92943 Norbert Schneider 08/2023 9881 norm(Mod(x,x^3-x-1)^760951-1) 92930 Paul Vanderveen 08/2022 9882 (2^308679+5)/1573 92919 Lelio R Paula 06/2013 9883 2^308650+513 92913 Lelio R Paula 02/2016 9884 5*7^109936+6 92908 Lelio R Paula 10/2014 9885 2*10^92897+89 92898 Robert Price 07/2016 9886 (19*23^68219-1867)/22 92896 Eric Chen 08/2023 9887 (2^308585+3182)/2 92894 Stefano Morozzi 09/2020 9888 (467307^16384+1)/2 92891 Richard Fischer 01/2021 9889 12^86073-29 92889 Lelio R Paula 06/2016 9890 2^308566-117 92888 Lelio R Paula 11/2012 9891 11594^22851-22851^11594 92872 Norbert Schneider 03/2022 9892 (17*10^92869-11)/3 92870 Robert Price 07/2015 9893 2^308459+75431 92856 Enzo Doria 04/2016 9894 2^308426-1866377 92846 Enzo Doria 03/2016 9895 24810^5521+5521^24810 92840 Hans Havermann 09/2020 9896 (96^46831-1)/95 92830 Paul Bourdelais 09/2017 9897 2^308349-112111 92823 Enzo Doria 06/2014 9898 9*10^92821+19 92822 Robert Price 05/2016 9899 2^308337-75 92819 Lelio R Paula 11/2012 9900 4*3^194508+7 92805 Lelio R Paula 08/2014 9901 22*25^66379-113 92796 Curtis Bright 05/2015 9902 24538^6047+6047^24538 92792 Hans Havermann 09/2020 9903 11^89101-1080 92790 Enzo Doria 12/2012 9904 2^308236-1867859 92789 Enzo Doria 04/2016 9905 12^85963+25 92770 Lelio R Paula 06/2016 9906 23692^8221+8221^23692 92753 Hans Havermann 08/2020 9907 7^109750-66 92750 Lelio R Paula 04/2016 9908 9*10^92742+11 92743 Robert Kinser 01/2017 9909 (2^308054+778)/2 92734 Stefano Morozzi 09/2020 9910 (21*2^308046-1)/8857 92729 Lelio R Paula 02/2014 9911 2^307997-110655 92717 Enzo Doria 05/2014 9912 L(443609) 92709 Renaud Lifchitz 11/2003 9913 10^92691+9 92692 Robert Price 03/2011 9914 10^92691-252291 92691 Patrick De Geest 08/2013 9915 (2^307883+3506)/2 92682 Stefano Morozzi 09/2020 9916 2^307879-2521 92681 Yves Minet 07/2014 9917 21269^21412+21412^21269 92666 Norbert Schneider 04/2020 9918 (2^307780-7)/19959669 92644 Lelio R Paula 06/2013 9919 14^80831+47 92643 Lelio R Paula 06/2016 9920 15^78744+92 92611 Lelio R Paula 07/2016 9921 65^51083-64 92610 Norbert Schneider 11/2014 9922 (2^307639+506)/2 92609 Stefano Morozzi 09/2020 9923 131^43737-130 92604 Norbert Schneider 02/2019 9924 6^118996-16943 92597 Enzo Doria 02/2013 9925 (16*10^92591+41)/3 92592 Robert Price 10/2017 9926 (2^307566+3094)/2 92587 Stefano Morozzi 09/2020 9927 (2^307528+1578)/2 92575 Stefano Morozzi 09/2020 9928 9*10^92573+83 92574 Robert Price 11/2020 9929 (3^194014-7)/2 92568 Lelio R Paula 04/2013 9930 (2^307498+570)/2 92566 Stefano Morozzi 09/2020 9931 (63^51439+1)/64 92555 Paul Bourdelais 08/2017 9932 (26*10^92546-77)/3 92547 Robert Price 02/2017 9933 3^193954+340 92540 Lelio R Paula 04/2016 9934 2^307407-307407^2 92539 Henri Lifchitz 05/2005 9935 24299^6430+6430^24299 92536 Hans Havermann 08/2020 9937 (17*10^92513-11)/3 92514 Robert Price 07/2015 9936 2^307322-399071 92514 Harrison Mesh 06/2022 9938 2^307318-4211 92512 Yves Minet 06/2011 9939 2^307280+193 92501 Lelio R Paula 11/2012 9940 20^71075-33 92471 Lelio R Paula 05/2016 9941 2^307126-78795 92455 Lelio R Paula 02/2016 9942 2^307125-49789 92454 Henri Lifchitz 08/2005 9943 fibonacci(442372)-2 92450 Jon Grantham 08/2023 9944 2^307099+23 92447 Lelio R Paula 11/2012 9945 129^43798+128 92440 Norbert Schneider 01/2019 9946 21826^17181+17181^21826 92435 Hans Havermann 09/2020 9947 Phi(277314,10)/3327769 92430 Makoto Kamada 05/2019 9948 (2^307022+1038)/2 92423 Stefano Morozzi 09/2020 9949 7*10^92414-69 92415 Robert Price 01/2017 9950 (9787*2^306975-1)/2129155 92407 Lelio R Paula 04/2015 9951 22280^14037+14037^22280 92402 Hans Havermann 09/2020 9952 2^306915+1873373 92391 Enzo Doria 06/2016 9953 2^306908+12915 92389 Lelio R Paula 02/2016 9954 21620^18759+18759^21620 92387 Hans Havermann 09/2020 9955 10^92386+111 92387 Jeppe Stig Nielsen 02/2023 9956 (2^306897+1142)/2 92385 Stefano Morozzi 09/2020 9957 19^72244-80 92383 Lelio R Paula 06/2016 9959 2^306849+75 92371 Lelio R Paula 11/2012 9958 (397*10^92369+53)/9 92371 Robert Price 11/2017 9960 2^306813-869688105 92360 Lelio R Paula 08/2016 9961 (2^306797+2694)/2 92355 Stefano Morozzi 09/2020 9962 21713^17914+17914^21713 92350 Hans Havermann 09/2020 9963 2^306672-109059 92318 Enzo Doria 04/2014 9964 (430463^16384+1)/2 92307 Richard Fischer 09/2020 9965 98*10^92295-9 92297 Robert Price 05/2023 9966 6^118604-17063 92292 Enzo Doria 02/2013 9967 21969^15878+15878^21969 92288 Hans Havermann 08/2020 9968 21690^17959+17959^21690 92276 Hans Havermann 08/2020 9969 (7613^23773-1)/7612 92273 Serge Batalov 08/2020 9970 (31*2^306487-1)/2291 92260 Lelio R Paula 02/2014 9971 2^306467-1835611 92256 Enzo Doria 04/2015 9972 2^306433+76427 92246 Enzo Doria 05/2016 9973 2^306430-113313 92245 Enzo Doria 07/2014 9974 (23*10^92244-59)/9 92245 Robert Price 03/2017 9975 (47*2^306398+1)/1384803 92231 Lelio R Paula 04/2015 9976 21436^20043+20043^21436 92217 Hans Havermann 09/2020 9977 (25*10^92186+59)/3 92187 Robert Price 05/2016 9978 2^306213-286183 92180 Enzo Doria 06/2015 9979 10^92178+61 92179 Robert Price 04/2011 9980 10^92178-175509 92178 Patrick De Geest 07/2013 9981 2^306200+1185 92176 Lelio R Paula 02/2016 9982 (2^306171+1514)/2 92167 Stefano Morozzi 09/2020 9983 2^306153+11 92162 Lelio R Paula 11/2012 9984 (2^306141-7)/5 92157 Lelio R Paula 06/2013 9985 21725^17454+17454^21725 92156 Hans Havermann 09/2020 9986 (26*10^92152-23)/3 92153 Robert Price 08/2016 9987 (2*10^92152+67)/3 92152 Robert Price 04/2017 9988 640*27^64370+17 92140 Eric Chen 02/2023 9989 21368^20457+20457^21368 92115 Hans Havermann 08/2020 9990 (2^305996+3018)/2 92114 Stefano Morozzi 09/2020 9991 4*10^92099+3*7^92099 92100 Mike Oakes 12/2010 9992 30504^1045+1045^30504 92096 Hans Havermann 08/2020 9993 24334^6085+6085^24334 92087 Hans Havermann 08/2020 9994 (2^305898+2262)/2 92085 Stefano Morozzi 01/2021 9995 (4591^25147-1)/4590 92083 Serge Batalov 08/2020 9996 115^44684+114 92081 Norbert Schneider 07/2018 9997 (416771^16384+1)/2 92077 Richard Fischer 08/2020 9998 (2^305867-2^152934+1)/5 92075 11/2006 9999 2^305851-109495 92071 Enzo Doria 04/2014 10000 (416213^16384+1)/2 92067 Richard Fischer 08/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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